Pressure drop formula
The Darcy-Weisbach equation gives the pressure lost to friction as fluid flows through a pipe. It depends on the friction factor, the pipe length and diameter, and the kinetic energy of the flow.
Variables
| ΔP | Pressure drop | Pa |
| f | Darcy friction factor | dimensionless |
| L | Pipe length | m |
| D | Pipe diameter | m |
| ρ | Fluid density | kg/m³ |
| v | Flow velocity | m/s |
Rearranged
Worked example
Water (ρ = 1000) flows at 2 m/s through 50 m of 0.1 m pipe, friction factor 0.02.
ΔP = 0.02 × (50 / 0.1) × (1000 × 2² / 2) = 0.02 × 500 × 2000.
Pressure drop grows with the square of velocity and in proportion to length, so doubling the flow speed quadruples the loss. The friction factor comes from the Reynolds number and the pipe relative roughness, usually read from a Moody chart or the Colebrook equation.
Need the friction factor inputs?
See the Reynolds Number Flow Regimes chart and the Pipe Roughness Values chart.
Darcy-Weisbach explained
The equation splits pressure loss into three parts: a friction factor capturing the pipe surface and flow regime, a length-to-diameter ratio capturing the pipe geometry, and the dynamic pressure capturing the flow energy. It applies to laminar and turbulent flow alike, with only the friction factor changing between them.
Finding the friction factor
In laminar flow the friction factor is simply 64 divided by the Reynolds number. In turbulent flow it depends on both the Reynolds number and the relative roughness, found from a Moody chart or solved with the Colebrook equation. Getting the friction factor right is usually the hardest part of a pressure-drop calculation.
FAQ
What is the Darcy-Weisbach equation?
It gives pipe friction pressure drop as the friction factor times length over diameter times the dynamic pressure, rho v squared over two.
How does velocity affect pressure drop?
Pressure drop scales with the square of velocity, so doubling the flow speed roughly quadruples the friction loss.
Where does the friction factor come from?
From the Reynolds number and the pipe relative roughness, read off a Moody chart or computed with the Colebrook equation.